In the curriculum, tracking risk or error is defined as “More specifically, tracking risk is defined as the standard deviation of the portfolio’s active return, where the active return for each period is defined as: Active return = Portfolio’s return - Benchmark index’s return” (page 327) The steps to calculate tracking risk are given as: 1. Find portfolio return and index return for each period 2. Subtract Index Return (IR) from Portfolio Return (PR) to get Active Return (AR) 3. Subtract AR of each period from Average AR of total sample periods 4. Square of AR - Avg. AR 5. Sum the squared difference 6. Divide by n - 1 7. Take square root to get standard deviation of active return Further, on page 330, in Solution to Example 3, in Solution to 1, it is given that “the target tracking risk of 1 percent means that the objective is that in at least two-thirds of the time periods, the return on the Star Bond Index Fund (portfolio in this case) is within plus or minus 1 percent of the return on the benchmark Lehman Brothers Global Aggregate Bond Index.” I think this interpretation is in contradiction with the definition given above on page 327. The tracking error should be standard deviation around the mean AR, not around benchmark return. If one has to calculate the risk around benchmark return, then I think instead of doing steps 3 and 4 above, one should just take square of AR, as the target active return should be 0, as we want to match the portfolio return to benchmark return. The tracking error, according to method given in the curriculum, may be understated. What do you guys think? I’m not sure but I think it should be like this. I might be wrong and that’s why, need your comments. Thanks.
You’re right, but there is an assumption there that the mean active return is 0 which is not a terrible assumption (since it’s probably 0 - transactions costs or thereabouts)
By and large, the mean active return has been negative, for most of the managers since it’s really difficult to beat the market after taking into account the benchmark drag. But I guess no such assumption was given in CFAI curriculum.